The range of a Lévy process
type: Item
instance of: scholarly article
title: The range of a Lévy process
zbMATH Open document ID: 0723.60039
author: Thomas Mountford
author: Sidney C. Port
published in: The Annals of Probability
publication date: 1991-01-01T00:00:00Z
review text: It is shown that all Lévy processes on the line whose paths are of bounded variation have a closed range over any finite time interval that is nowhere dense except for those processes having positive (negative) drift with Lévy measure finite on (0,\(\infty)\) (finite on (- \(\infty,0))\). The proof is relied upon M. T. Barlow's 0-1 law and the fact that any cadlag process which fails to hit points has nowhere dense closed range over any finite time interval.
reviewed by: Ilya S. Molchanov
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4192773
zbMATH Keywords: sample paths
zbMATH Keywords: independent increments
zbMATH Keywords: Lévy processes
zbMATH Keywords: cadlag process
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176990541
OpenAlex ID: W2045810838
DOI: 10.1214/AOP/1176990541
description: scientific article; zbMATH DE number 4192773